What is the greatest common factor of 12a2b3

Question

and 18a3b
?(1 point)
Responses

6ab2
6 a b superscript 2 baseline

12a5b4
12 a superscript 5 baseline b superscript 4 baseline

6a2b
6 a superscript 2 baseline b

12a2b

Answer 1

To find the greatest common factor (GCF) of the expressions \( 12a^2b^3 \) and \( 18a^3b \), we will break down both numbers and variables.

1. Numerical Coefficients:

   • The numerical coefficients are \( 12 \) and \( 18 \).
   • The factors of \( 12 \) are \( 1, 2, 3, 4, 6, 12 \).
   • The factors of \( 18 \) are \( 1, 2, 3, 6, 9, 18 \).
   • The GCF of \( 12 \) and \( 18 \) is \( 6 \).

2. Variable Part:

   • For \( a \), we have \( a^2 \) and \( a^3 \). The GCF is \( a^{\min(2, 3)} = a^2 \).
   • For \( b \), we have \( b^3 \) and \( b^1 \). The GCF is \( b^{\min(3, 1)} = b^1 \) or simply \( b \).

Combining these results, we find the greatest common factor (GCF) is:

\[ 6a^2b^1 = 6a^2b \]

Thus, the greatest common factor of \( 12a^2b^3 \) and \( 18a^3b \) is \( 6a^2b \).

The correct response from the options provided is:

6 a superscript 2 baseline b.